Question

Problem 10-26 As part of an insurance company’s training program, participants learn how to conduct an analysis of clients’ insurability. The goal is to have participants achieve a time in the range of 32 to 47 minutes. Test results for three participants were: Armand, a mean of 38.0 minutes and a standard deviation of 2.0 minutes; Jerry, a mean of 35.0 minutes and a standard deviation of 3.0 minutes; and Melissa, a mean of 39.5 minutes and a standard deviation of 1.7 minutes. a.Which of the participants would you judge to be capable? (Do not round intermediate calculations. Round your answers to 2 decimal places.)

Answer 1

We need to determine the process capability index (Cpk) of each candidate

Cpk = MIN((USL-$\mu$)/3$\sigma$, ($\mu$-LSL)/3$\sigma$)

Cpk of Armand = MIN((47-38)/(3*2), (38-32)/(3*2))

= 1

Cpk of Jerry = MIN((47-35)/(3*3), (35-32)/(3*3))

= 0.33

Cpk of Melissa = MIN((47-39.5)/(3*1.7), (39.5-32)/(3*1.7))

= 1.47

Cpk of Melissa is the highest and is also greater than 1.33. Therefore, Melissa would be judged as capable.